An overview of theory and practice on process capability indices for quality assurance

Chien Wei Wu*, W.l. Pearn, Samuel Kotz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

226 Scopus citations


Process capability indices (PCIs), Cp, Ca, Cpk, Cpm, and Cpmk have been developed in certain manufacturing industry as capability measures based on various criteria, including process consistency, process departure from a target, process yield, and process loss. It is noted in certain recent quality assurance and capability analysis works that the three indices, Cpk, Cpm, and Cpmk provide the same lower bounds on the process yield. In this paper, we investigate the behavior of the actual process yield, in terms of the number of non-conformities (in ppm), for processes with fixed index values of Cpk=Cpm=Cpmk, possessing different degrees of process centering. We also extend Johnson's [1992. The relationship of Cpm to squared error loss. Journal of Quality Technology 24, 211-215] result formulating the relationship between the expected relative squared loss and PCIs. Also a comparison analysis among PCIs is carried out based on various criteria. The result illustrates some advantages of using the index Cpmk over the indices Cpk and Cpm in measuring process capability (yield and loss), since Cpmk always provides a better protection for the customers. Additionally, several extensions and applications to real world problem are also discussed. The paper contains some material presented in the Kotz and Johnson [2002. Process capability indices-a review, 1992-2000. Journal of Quality Technology 34(1), 1-19] survey but from a different perspective. It also discusses the more recent developments during the years 2002-2006.

Original languageEnglish
Pages (from-to)338-359
Number of pages22
JournalInternational Journal of Production Economics
Issue number2
StatePublished - 1 Feb 2009


  • Expected relative loss
  • Fraction non-conforming
  • Process capability indices
  • Process consistency
  • Process relative departure
  • Quality assurance

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